The invention relates to the general field of telecommunications, and in particular to the field of digital communications.
The invention relates more particularly to transmitting and receiving signals made up of data symbols by means of a digital communications system having multiple receive antennas, also known as a single input multiple output (SIMO) system when the system has only one transmit antenna or as a multiple input multiple output (MIMO) system when the system has a plurality of transmit antennas.
The invention thus applies in preferred manner to wireless communications, e.g. on a fourth generation or future generation network (e.g. long-term evolution (LTE) networks) as defined in the third generation partnership project (3GPP) standard, or on optical transmission networks. The invention applies equally well in downlink (from a base station to a terminal) or in uplink (from a terminal to a base station).
The invention also applies in preferred manner to a frequency-flat propagation channel, i.e. a channel without echo (also known as a “single tap” channel or a “flat fading” channel).
In known manner, multi-antenna systems enable very high transmission rates to be achieved, with the capacity of MIMO channels increasing in proportion to the minimum number of transmit antennas and of receive antennas.
Among such multi-antenna systems, systems that use a large number of antennas (also known as “large scale multiple antenna arrays”), typically having of the order of one hundred or several hundreds of antennas, which may be colocated on a single site or distributed geographically, offer numerous advantages such as, in particular, higher data rates, greater reliability of transmission, energy savings, etc.
Various data symbol transmission techniques have been proposed for MIMO systems in the context of a single-carrier system with a flat fading channel.
In the particular circumstance of a flat fading channel, the propagation channel between any one antenna of the transmitter and any one antenna of the receiver may be modeled by means of a complex gain. As a result, the propagation channel between a transmitter having a plurality of transmit antennas and a receiver having a plurality of receive antennas can be written in the form of a complex matrix, referred to as the MIMO propagation channel matrix, in which each row corresponds to a receive antenna and each column corresponds to a transmit antenna.
Among those techniques, some rely on knowledge of the MIMO propagation channel matrix on transmission. This channel knowledge makes it possible to calculate a focusing or “beamforming” matrix Q that is applied to the data symbols before they are transmitted by the transmit antennas. This precoding matrix enables each data symbol to be focused on a particular receive antenna in order to facilitate decoding of the received data symbols on reception.
Various forms of focusing precoding can be envisaged on transmission. Thus, by way of example, it is possible to consider performing focusing precoding by time reversal. With a flat fading channel, time reversal consists in using as the focusing matrix the conjugate transpose of the MIMO propagation channel matrix.
In the description below, the concept of the transmission or propagation channel between transmit and receive antennas is used to cover not only the effects of the media over which the digital signal propagates between the transmit and receive antennas (e.g. a radio channel or a wired connection), but also the effects that are induced by the transmit and receive antennas on the digital signal.
Implementing such a precoding matrix on transmission makes it possible to use a simple equalization scheme for each antenna on reception. The equivalent channel matrix that results from multiplying the precoding matrix by the MIMO propagation channel matrix is a matrix that is quasi-diagonal. Consequently, no complex matrix inversion is needed on reception in order to decode the signal received over the received antennas.
Furthermore, obtaining the precoding matrix does not require complex matrix inversion to be performed on transmission (all that is required is the conjugate transpose of the MIMO channel matrix). Such a transmission scheme is thus particularly well adapted to MIMO systems based on large antenna arrays.
Nevertheless, it may be observed that with that transmission scheme, interference remains between data symbols on reception (which interference corresponds to the non-zero non-diagonal terms in the matrix of the equivalent channel), and this has an impact on performance. In other words, with that transmission scheme, each symbol is focused on a distinct target receive antenna, thereby creating a focal spot that is centered on the target antenna, but that interferes with neighboring receive antennas.
Other MIMO transmission systems have been proposed to reduce residual inter-symbol interference. By way of example, such systems are based on using precoders:                of the zero forcing (ZF) type: such precoders serve to cancel the non-diagonal terms of the matrix of the equivalent channel, so that the focal spot centered on the target receive antenna presents zero interference with the neighboring antennas; or        that minimize mean square error (MMSE).        
Nevertheless, those systems require complex matrix operations to be performed on reception, in particular operations that involve inverting matrices. Unfortunately, firstly there is no guarantee that such inversions are feasible, and secondly such matrix inversions cannot be performed in practice for a large number of antennas.
There therefore exists a need for a digital transmission scheme that can be used in the context of multi-antenna arrays having a large number of antennas and avoiding the drawbacks of the state of the art.